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math.AC2017★ 63 cited
Tensor rank is not multiplicative under the tensor product
Matthias Christandl, Asger Kjærulff Jensen, Jeroen Zuiddam
The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an l-tensor. The tensor product…
math.AC2015★ 14 cited
A note on the gap between rank and border rank
Jeroen Zuiddam
We study the tensor rank of the tensor corresponding to the algebra of n-variate complex polynomials modulo the dth power of each variable. As a result we find a sequence of tensor…